Sine Function Calculator

Background.

Sine is the function that turns an angle into a height. Picture a point travelling round a circle of radius 1, starting at the far right and moving anticlockwise: the sine of the angle it has swept through is simply how far above the centre it sits. At 0° it is level with the centre, so the sine is 0; at 90° it is at the top, sine 1; at 180° it is level again, at 270° it reaches the bottom at −1, and after a full turn the pattern repeats. Plot that height against the angle and you get the sine wave, the shape behind alternating current, sound and anything else that oscillates smoothly.

For angles between 0° and 90° the same number has a triangle meaning: in a right triangle, the sine of an angle is the side opposite it divided by the hypotenuse. A 6 m ladder leaning at 75° to the ground reaches about 6 × 0.9659 = 5.796 m up the wall, and 100 m along a road climbing at 5° raises you about 8.716 m.

The page takes the angle in degrees, converts it to radians by multiplying by π/180, and evaluates the sine. That conversion is where most hand-calculator mistakes come from. Spreadsheets and programming languages expect radians, and so does a scientific calculator left in radian mode, which is how sin(30) turns into about −0.988 instead of 0.5. Here the input is always degrees.

Negative angles and angles beyond a full turn are accepted, from −3,600° to 3,600°, since 390° and 30° describe the same position on the circle. What the page does not do is run backwards. Finding an angle from a sine is ambiguous, because 30° and 150° share the value 0.5, and needs the inverse sine plus a decision about which angle you mean.

What is sine function calculator?

The sine of an angle θ is the vertical coordinate of the point reached by rotating through θ anticlockwise from the positive x-axis around a circle of radius 1. For acute angles this equals the ratio of the opposite side to the hypotenuse in any right triangle containing θ. As a function, sine accepts any real angle and returns a value between −1 and 1, repeating every 360°. It is odd, so sin(−θ) = −sin θ, and it satisfies sin(180° − θ) = sin θ, which is why each value strictly between −1 and 1 occurs at two angles in every turn.

How to use this calculator.

1. 01Type the angle in degrees into Angle. Decimal degrees work directly; convert minutes and seconds first, so 37° 30′ becomes 37.5.
2. 02If your angle is in radians, multiply it by 180/π, about 57.2958, before entering it.
3. 03Enter clockwise angles as negative numbers and angles past a full turn as they are; anything from −3,600° to 3,600° is accepted.
4. 04Read sin(angle) as a plain ratio. In a right triangle, multiply it by the hypotenuse to get the side opposite the angle.

The formula.

sin(θ in degrees) = sin(θ × π/180). A full turn is 360° or 2π radians, so one degree is π/180, about 0.0174533 radians. The conversion re-expresses the angle in the unit sine is naturally defined in, where an angle is the length of arc it cuts from a circle of radius 1, and the sine is then evaluated on that radian value. Close to 0° the sine is almost equal to the angle in radians (sin 1° is 0.0174524 against 0.0174533), the basis of the small-angle approximation used for pendulums and optics. How sensitive the answer is depends on where you are on the circle: near 0° and 180° each extra degree shifts the sine by about 0.0175, while near 90° and 270° the curve is almost flat and a degree of error in the angle barely changes the result.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Rice University. College Algebra 2e, 2021. Algebra and function chapters. Retrieved 2026-08-06.
2. [2]OpenStax, Rice University. Precalculus 2e, 2021. Trigonometry and analytic geometry chapters. Retrieved 2026-08-06.
3. [3]NIST/SEMATECH. e-Handbook of Statistical Methods, 2012. Chapter 1.3 and Chapter 4. Retrieved 2026-08-06.